2) It is known that, on average, a predatory fish catches 1 prey in 10 minutes. Find the
probability that the fish will catch 8 preys in an hour.
2) It is known that, on average, a predatory fish catches 1 prey in 10 minutes. Find the
probability that the fish will catch 8 preys in an hour.
If X is a random variable with the following probability density function: (𝑥) = { 2 |𝑥| 1 0 Determine: a. c value b. E(X) c. Var(X) d. P( X > )
A cog making machine turns out three defective cogs for every two hundred cogs produced.
What is the probability that any two cogs will turn out defective?
What is the probability that a randomly selected student is a female? *
1 point
A.11/3
B.77/12
C.55/11
D.88/15
The joint probability distribution of two random variables X and Y is given in the following table.
Y | |||
-1 | 2 | ||
X | -1 | 0.1 | 0.1 |
-2 | 0.5 | 0.1 |
1. Calculate the marginal probability distribution of X.
2. Calculate the marginal probability distribution of Y.
3. Calculate E( X ) and s.d.( X ).
4. Calculate E( Y ) and s.d.( Y )
5. Calculate cov(X, Y) and corr(X, Y).
6. Calculate the conditional probability distribution of X given Y = -1.
7. Calculate the conditional probability distribution of X given Y = 2.
8. Calculate E( X | Y = -1 ) and var( X | Y = -1 ).
9. Calculate E( X | Y = 2 ) and var( X | Y = 2 ).
10. Verify the Law of Iterated Expectations E(X)=E[E(X|Y)] by using your previous results.
11. Are X and Y independent random variables? Justify your answer based on answers to the preceding questions.
70% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 31 owned dogs are randomly selected, find the probability that
a. Exactly 20 of them are spayed or neutered.
b. At most 24 of them are spayed or neutered.
c. At least 22 of them are spayed or neutered.
d. Between 16 and 23 (including 16 and 23) of them are spayed or neutered.
Round all answers to 4 decimal places.
Sharon draws a random card, from a regular deck of cards, and rolls a regular 6 sided die. What is the probability that Sharon draws a card that is a Heart and rolls a 3?
Toss 5 coins 20 times Simultaneously and Observe the number of heads that will occur. The Possible Values of X or The number of heads in 5 coins tossed are 0, 1,2,3,4 and 5.